Adding Modifier (Mirrored)
You mirror in the X direction (along the X axis). From your screenshot, the center of your object is in the middle of the 'left' side, which means that the original and generated (mirrored) points overlap.
Selecting the Y axis as mirror axis probably does what you want.

If you already applied the mirror modifier, you might also want to 'remove doubles' to get rid of superfluous vertices (which can give strange effects with e.g. subdivision or bevel modifiers)